where \(M_{\rm Fe,500}\)  is the iron mass enclosed within \(r_{500}\)  in the ICM/IGrM, \(M^{\rm star}_{\rm Fe,500}\)  is the iron mass locked into stars, \(M_{\rm star,500}(0)\)  is the mass of gas that went into stars whose present mass is reduced to \(M_{\rm star,500}\)  by the mass return from stellar mass loss, i.e. \(M_{\rm star,500}(0) = r_o M_{\rm star,500}\) , where \(r_o\)  is the return factor. We take \(r_o = 1/0.58 \)  following [1]} and [2]}. A caveat should be made that the iron yield can be matched to a theoretical prediction only if we are able to make a full inventory under the assumption of a closed system. If iron can leave the system or just does not reside within the radius used to make the estimate we can not draw a conclusive inference. This is particularly the case at the scale of groups as we discuss further in this section.
